16 March, 2016

GIS

Geographic Information Systems

GIS

Geographic Information Systems

  • incorporating
  • storing
  • manipulating
  • analyzing
  • displaying…

Spatial Data

What is spatial data?

Nonspatial data has no location information

nonspatial = data.frame(
  id=c(1,2,3,4),
  data=rnorm(4)
)
print(nonspatial)
##   id       data
## 1  1 -0.1140578
## 2  2  1.0914729
## 3  3 -0.4780712
## 4  4  0.1558649

What is spatial data?

Spatial data has location information

The simplest spatial data are points on a map

spatial = data.frame(
  id=c(1,2,3,4),
  data=rnorm(4),
  x=runif(4,-180,180),
  y=runif(4,-90,90)
)
print(spatial)
##   id        data           x         y
## 1  1 -1.06768167    8.198913  45.85735
## 2  2 -0.36974434  103.754462 -84.13661
## 3  3  0.03500162 -124.050690  39.74547
## 4  4  0.41151930   43.201727 -40.59028

What is spatial data?

Which we can convert to explicitly spatial data using the sp package. Most GIS packages in R store data as sp classes.

library(sp)

What is spatial data?

The sp package has a method called coordinates that converts points to an sp class.

coordinates(spatial) = ~ x + y
class(spatial)
## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"
plot(spatial, axes=T)


What is spatial data?

Spatial data also needs a reference system or "projection" that allows us to represent spatial features on a map. Projections can be thought of as simply a coordinate system with an origin that is relative to a known point in space.

This is a whole field of mathematically intensive study termed "geodesy"

Much of the field of geodesy is jam-packed in the rgdal package, which is a wrapper for the Geospatial Data Abstration Library

library(rgdal)

What is spatial data?

rgdal includes a comprehensive list of projections that are typically represented as a string of parameters.

The most common is our standard latitude/longitude system, where the coordinates are angular and the origin is the equator directly south of Greenwich, England. The simplest projection string to denote this projections is:

"+proj=longlat"

To define the projection for spatial, we write to its proj4string slot:

proj4string(spatial) = "+proj=longlat"

Projections are a necessary evil for GIS users (to be continued)

What is spatial data?

With a projection associated with our spatial data, we can now relate it to other spatial data. In other words, let's make a map!

library(leaflet)
m = leaflet(data=spatial) %>%
  addTiles() %>%
  addMarkers()
m

What is spatial data?

Spatial data types

Spatial data types

Two main types: vector and raster

Vector = Polygons
Raster = Grid

Vector = Discrete
Raster = Continuous

Vector = Illustrator/Inkscape
Raster = Photoshop/GIMP







Vector Data

Intro

Vector I/O

library(rgdal)

Vector I/O

soils = readOGR(dsn="data", layer="soilsData")
## OGR data source with driver: ESRI Shapefile 
## Source: "data", layer: "soilsData"
## with 75 features
## It has 27 fields
writeOGR(
  soils,
  "data",
  "soilsData_out",
  driver="ESRI Shapefile"
)

Vector data structure

class(soils)
## [1] "SpatialPolygonsDataFrame"
## attr(,"package")
## [1] "sp"
slotNames(soils)
## [1] "data"        "polygons"    "plotOrder"   "bbox"        "proj4string"

Vector data structure

Take a peak here at the top of our attribute table

str(soils@data[,1:5])
## 'data.frame':    75 obs. of  5 variables:
##  $ mukey  : Factor w/ 25 levels "2774742","2774772",..: 12 19 12 6 9 5 7 24 25 13 ...
##  $ muarcrs: Factor w/ 75 levels "0.40538405","0.90105194",..: 25 62 70 19 3 29 20 7 5 27 ...
##  $ Sand1  : num  21.5 11 21.5 12 29.5 ...
##  $ Sand2  : num  35.29 8.34 35.29 9.02 38.22 ...
##  $ Sand3  : num  45.09 7.56 45.09 16.59 64.52 ...

*Make sure not to call head() or str() on a spatial object, as this spits out the first six features and all their attributes

Vector data structure

str(soils@data[,1:10])
## 'data.frame':    75 obs. of  10 variables:
##  $ mukey  : Factor w/ 25 levels "2774742","2774772",..: 12 19 12 6 9 5 7 24 25 13 ...
##  $ muarcrs: Factor w/ 75 levels "0.40538405","0.90105194",..: 25 62 70 19 3 29 20 7 5 27 ...
##  $ Sand1  : num  21.5 11 21.5 12 29.5 ...
##  $ Sand2  : num  35.29 8.34 35.29 9.02 38.22 ...
##  $ Sand3  : num  45.09 7.56 45.09 16.59 64.52 ...
##  $ Sand4  : num  48.6 30.6 48.6 36.7 33.2 ...
##  $ Sand5  : num  0 31.1 0 27.1 57.2 ...
##  $ Silt1  : num  45.8 65.2 45.8 68.7 54.5 ...
##  $ Silt2  : num  37.3 64.9 37.3 60.3 43.5 ...
##  $ Silt3  : num  36.7 64.1 36.7 34 21.1 ...

Vector data structure

str(soils@polygons[1])
## List of 1
##  $ :Formal class 'Polygons' [package "sp"] with 5 slots
##   .. ..@ Polygons :List of 1
##   .. .. ..$ :Formal class 'Polygon' [package "sp"] with 5 slots
##   .. .. .. .. ..@ labpt  : num [1:2] -90.1 43.1
##   .. .. .. .. ..@ area   : num 1.19e-06
##   .. .. .. .. ..@ hole   : logi FALSE
##   .. .. .. .. ..@ ringDir: int 1
##   .. .. .. .. ..@ coords : num [1:21, 1:2] -90.1 -90.1 -90.1 -90.1 -90.1 ...
##   .. ..@ plotOrder: int 1
##   .. ..@ labpt    : num [1:2] -90.1 43.1
##   .. ..@ ID       : chr "0"
##   .. ..@ area     : num 1.19e-06

Vector data structure

Number of features

length(soils)
## [1] 75

Vector data structure

Index the first feature with a slice

poly_1 = soils[1,]

Plotting

plot(
  soils,
  main="Soils from Western WI",
  col=rainbow(5)
)












Working with Vector Data

Raster Data

Intro

A raster grid is rectangular.

Grid is another word for matrix.

Grid is another word for image.

A GIS raster grid is a matrix/image with an associated location and projection.

Intro

At a minimum, a GIS raster grid contains:

  1. matrix of values
  2. projection
  3. reference point, often (x,y) of the lower-left corner
  4. cellsize









Raster I/O

The rgdal rgdal packages is primarily for I/O and projecting GIS data

library(rgdal)

The raster package does everything rgdal does, but it includes lots of additional functionality.

library(raster)

Raster I/O

elev = readGDAL("data/dem_wi.tif")
writeGDAL(elev, "data/dem_wi_out.tif")
elev = raster("data/dem_wi.tif")
writeRaster(elev, "data/dem_wi_out.tif")

Raster data structure

The raster object elev has all the necessary pieces of spatial information:

elev
## class       : RasterLayer 
## dimensions  : 284, 387, 109908  (nrow, ncol, ncell)
## resolution  : 0.01666667, 0.01666667  (x, y)
## extent      : -93.03262, -86.58262, 42.3949, 47.12823  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## data source : C:\Users\ruesca\Documents\GeRgraphyPresentation\data\dem_wi.tif 
## names       : dem_wi 
## values      : 175, 565.4104  (min, max)

Raster data structure

Which means we can make a map!

m = leaflet() %>%
  addTiles() %>%
  addRasterImage(elev, opacity=0.5)
m

Raster data structure

Raster analysis

Remember that rasters are just matrices!

Therefore, most matrix operations can be applied to rasters. For example:

plot(
  elev > 400,
  col=c("red", "blue")
)








Raster analysis

Rasters can be easily converted to matrices to do more complex work.

lat_grad = apply(
  as.matrix(elev),
  1,
  mean,
  na.rm=T
)
plot(lat_grad, type="l")






Raster overlay

Most raster analysis ultimately executes some sort of overlay.

The issue:

To overlay two or more rasters, their projections, extents, and cellsizes must align perfectly.

This can be a difficult task.

Raster overlay

coordinate systems

What is the highest point in each county?

# Pseudo-code
1. Read in elevation data (raster grid)
2. Read in county boundary data (polygons)
3. Convert counties to raster grid that aligns with elevation grid
4. Find maximum elevation gridcell within each county

Raster overlay

coordinate systems

counties = readOGR("data", "WI_Counties")
## OGR data source with driver: ESRI Shapefile 
## Source: "data", layer: "WI_Counties"
## with 72 features
## It has 7 fields
elev
## class       : RasterLayer 
## dimensions  : 284, 387, 109908  (nrow, ncol, ncell)
## resolution  : 0.01666667, 0.01666667  (x, y)
## extent      : -93.03262, -86.58262, 42.3949, 47.12823  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## data source : C:\Users\ruesca\Documents\GeRgraphyPresentation\data\dem_wi.tif 
## names       : dem_wi 
## values      : 175, 565.4104  (min, max)

Raster overlay

coordinate systems

proj4string(counties)
## [1] "+proj=tmerc +lat_0=0 +lon_0=-90 +k=0.9996 +x_0=520000 +y_0=-4480000 +ellps=GRS80 +units=m +no_defs"
proj4string(elev)
## [1] "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

Raster overlay

coordinate systems

extent(counties)
## class       : Extent 
## xmin        : 294839 
## xmax        : 770036.4 
## ymin        : 225108.8 
## ymax        : 734398.4
extent(elev)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

cty_grid = rasterize(counties, elev, field="COUNTY_FIP")
summary(cty_grid)
##          layer
## Min.        NA
## 1st Qu.     NA
## Median      NA
## 3rd Qu.     NA
## Max.        NA
## NA's    109908

Raster overlay

coordinate systems

prj = proj4string(elev)
cty_prj = spTransform(counties, prj)
To do this, we use the spTransform function in the sp package.

Raster overlay

coordinate systems

extent(cty_prj)
## class       : Extent 
## xmin        : -92.88924 
## xmax        : -86.8048 
## ymin        : 42.49197 
## ymax        : 47.08077
extent(elev)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

plot(elev)
plot(cty_prj, add=TRUE)














Raster overlay

coordinate systems

cty_grid = rasterize(cty_prj, elev, field="COUNTY_FIP")
summary(cty_grid)
##         layer
## Min.        1
## 1st Qu.    18
## Median     36
## 3rd Qu.    55
## Max.       72
## NA's    50557

Raster overlay

coordinate systems

extent(cty_grid)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823
extent(elev)
## class       : Extent 
## xmin        : -93.03262 
## xmax        : -86.58262 
## ymin        : 42.3949 
## ymax        : 47.12823

Raster overlay

coordinate systems

library(dplyr)
ovly = data.frame(
  elev=getValues(elev),
  cty=getValues(cty_grid)
)

hi_pt = ovly %>%
  group_by(cty) %>%
  mutate(
    elev = (elev == max(elev, na.rm=T)) * elev
  ) %>%
  ungroup()

elev = setValues(elev, hi_pt[["elev"]])
elev[elev == 0] = NA
hi_pt_sp = rasterToPoints(elev, spatial=T)

Raster overlay

coordinate systems